UNCERTAINTY AND ESTIMATION IN RECONSTRUCTABILITY ANALYSIS

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Abstract
The problem of identifying discrete probability distributions from partial information is examined. The study was motivated primarily by the identification problem of reconstructability analysis, in which the partial information takes the form of known marginal distributions. However, most of the concepts discussed apply more generally, when information is available in the form of arbitrary linear constraints on the components of a discrete probability distribution. These constraints arise naturally in many contexts (e.g., when bounds on the probabilities are known, or an ordering among some of them is determinable). Techniques for making inferences and decisions on the basis of the information available are developed and illustrated. It is argued that, in many cases, it is neither necessary nor desirable to estimate a single, numerically determinate distribution (e.g., the maximum entropy distribution) compatible with the constraints in order to utilize the information.

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